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Optimization History

The Optimization History page visualizes the evolution of variables, objectives, constraints, and observables throughout the optimization process, showing how solutions improved over iterations.

Overview

This page displays time series plots showing: - How design variables changed during optimization - Evolution of objective values - Constraint satisfaction over time - Observable values throughout the process

Key Use: Understand optimization dynamics and convergence behavior

Features

Result Selection

Select Result: Choose which optimization result to visualize - Currently supports single result selection - All plots update when you change the selection

Note: This page requires results with iteration/time information

Variable Selection

Select which variables to display in each category:

Design Variables: - Input parameters that were optimized - Shows how the optimizer explored the design space - Default: First 3 variables selected

Objectives: - Optimization goals being minimized/maximized - Shows improvement over time - Default: First 3 objectives selected

Constraints: - Inequality and equality constraints - Shows feasibility evolution - Default: First 3 constraints selected

Observables: - Additional computed or measured values - Shows derived metrics over time - Default: First 3 observables selected

Plot Types

Time Series Plots

Standard Mode (for \<10,000 iterations): - Full resolution plots - All data points visible - Interactive hover and zoom

Resampled Mode (for >10,000 iterations): - Automatically activated for large datasets - Maintains visual fidelity while improving performance - Uses plotly-resampler for efficient rendering

Constraint Plots

Special visualization for constraints: - Feasibility Shading: Background shows feasible region - Threshold Lines: Shows constraint limits (0 for inequality) - Violation Highlighting: Clearly shows when constraints are violated

Understanding the Plots

Design Variables Plot

What it Shows: - How each design variable changed over iterations - Exploration patterns - Convergence behavior

Interpretation: - Flat lines: Variable converged early - Oscillations: Active search in that dimension - Trends: Directional improvement - Jumps: Major design changes or restarts

Objectives Plot

What it Shows: - Objective values at each iteration - Improvement trajectory - Convergence to optimal values

Interpretation: - Downward trend (minimization): Improvement - Upward trend (maximization): Improvement - Plateaus: Convergence or local optimum - Spikes: Exploration or constraint violations

Constraints Plot

What it Shows: - Constraint values over time - Feasibility status - Constraint violations

Interpretation: - Values ≤ 0: Feasible (for inequality constraints) - Values > 0: Constraint violation - Approaching 0: Active constraint - Far from 0: Inactive constraint

Visual Aids: - Green shading: Feasible region - Red shading: Infeasible region - Horizontal line at 0: Feasibility threshold

Observables Plot

What it Shows: - Evolution of computed or measured values - Derived metrics over time - System behavior indicators

Interpretation: - Depends on specific observable - Look for trends and patterns - Correlate with objectives and variables

Usage Workflows

Workflow 1: Convergence Analysis

  1. Select your result
  2. View objectives plot
  3. Identify when objectives stopped improving
  4. Check if optimization converged
  5. Assess solution quality

Look For: - Clear convergence to stable values - Continued improvement vs plateau - Oscillations indicating non-convergence

Workflow 2: Constraint Handling

  1. Select relevant constraints
  2. View constraints plot
  3. Identify when feasibility was achieved
  4. Check for persistent violations
  5. Understand constraint activity

Look For: - Transition from infeasible to feasible - Active constraints (values near 0) - Constraint violations over time

Workflow 3: Design Space Exploration

  1. Select design variables
  2. View variables plot
  3. Observe exploration patterns
  4. Identify important variables
  5. Understand optimizer behavior

Look For: - Variables that changed significantly - Variables that converged early - Exploration vs exploitation phases

Workflow 4: Multi-Objective Dynamics

  1. Select all objectives
  2. View objectives plot
  3. Observe trade-off evolution
  4. Identify when Pareto front was reached
  5. Understand objective conflicts

Look For: - Competing objectives (one improves, another worsens) - Synergistic objectives (both improve together) - Pareto front approximation over time

Best Practices

Variable Selection

Start with Objectives: - Always view objectives first - Understand overall performance - Identify optimization success

Add Variables Selectively: - Focus on most important variables - Too many lines create clutter - Add variables based on findings

Include Constraints: - Always check feasibility evolution - Understand constraint impact - Identify problematic constraints

Analysis Approach

Sequential Analysis: 1. Objectives: Did it improve? 2. Constraints: Is it feasible? 3. Variables: How did it get there? 4. Observables: What else changed?

Comparative Analysis: - Compare early vs late iterations - Identify phases of optimization - Understand algorithm behavior

Interpretation

Convergence Indicators: - Objectives plateau - Variables stabilize - Constraints satisfied - Observables steady

Problem Indicators: - Objectives not improving - Persistent constraint violations - Erratic variable behavior - Unexpected patterns

Common Patterns

Successful Optimization

Characteristics: - Objectives improve steadily - Variables converge to stable values - Constraints become satisfied - Clear convergence point

Example: - Initial exploration (high variation) - Improvement phase (objectives decrease) - Refinement phase (small adjustments) - Convergence (stable values)

Struggling Optimization

Characteristics: - Objectives oscillate without improvement - Variables jump around - Constraints repeatedly violated - No clear convergence

Possible Causes: - Poor algorithm settings - Difficult optimization landscape - Conflicting objectives - Tight constraints

Multi-Phase Optimization

Characteristics: - Distinct phases visible in plots - Sudden changes in behavior - Multiple convergence attempts

Interpretation: - Algorithm restarts - Phase transitions - Adaptive strategies

Advanced Features

Plotly Resampler

For large datasets (>10,000 iterations):

Benefits: - Maintains visual quality - Improves performance - Enables smooth interaction

Usage: - Automatically activated - Transparent to user - Zoom and pan work normally

Interactive Features

Zoom and Pan: - Click and drag to zoom - Pan to explore different time ranges - Double-click to reset

Hover Information: - Hover over lines for exact values - See iteration number - Compare multiple variables

Legend: - Click to show/hide variables - Double-click to isolate one variable - Useful for complex plots

Tips and Tricks

Visualization

Focus on Key Periods: - Zoom to early iterations for exploration phase - Zoom to late iterations for convergence - Compare different time ranges

Isolate Variables: - Use legend to hide/show specific variables - Focus on one or two at a time - Reduce visual clutter

Export Plots: - Download for reports - Include in presentations - Document optimization behavior

Analysis

Identify Phases: - Look for distinct behavioral changes - Mark important iterations - Understand algorithm strategy

Correlate Plots: - Compare variables with objectives - Link constraint violations to objective changes - Understand cause and effect

Validate Convergence: - Check if values truly stabilized - Look for continued small improvements - Assess if more iterations needed

Troubleshooting

Plots Not Showing

  • Ensure result has iteration data
  • Check that variables are selected
  • Verify result is properly loaded

Too Many Lines

  • Reduce number of selected variables
  • Use legend to hide some lines
  • Focus on most important variables

Can't See Patterns

  • Try zooming to specific time ranges
  • Adjust number of visible variables
  • Check axis scales

Performance Issues

  • Resampler should activate automatically for large datasets
  • If slow, try reducing number of plots
  • Close other browser tabs
  • Path: /optimization-history
  • Category: Visualization
  • Icon: Chart line icon
  • Requires Data: Yes (with iteration information)